# trigonometry

1. ### Velocity of separation: How fast is the distance between two cars is changing?

Hello, A Land cruiser drives east from point A at 40 kph. Another car Ford Expedition, starting from B at the same time , drives northwest $30^\circ$ towards A at 60 kph. B is 40 km from A. How fast in kph is the distance between two cars changing after 47 minutes? Solution:- My attempt: I...
2. ### Diameter of an asteroid

I cannot figure out this astronomy problem. Suppose the average mass of each of 20000 asteroids in the solar system is 10^17kg. Assuming a spherical shape and a density of 2830 kg/m^3, estimate the diameter of an asteroid having this average mass. I need to find diameter in km. Thank you for...
3. ### Why this equation is true? Can someone explain?

Can someone explain why this equation is true? I came up with it some time ago and did not understand why it's true: Is there some specific rule for that? Maxima CAS could not tell if it's true, but it is.(Surprised) \frac{2 \tan{\left( \frac{\alpha }{2}\right) }}{\tan{\left( \alpha \right)...
4. ### I need help justifying a quotient of two trig functions

I know (1-cos2(x/2))1/2/(1-cosx)1/2 Is equal to 1/root2 but I don't know a formal method for justifying this, so I'm asking for someone to show me how to show my teacher that it's a true identity
5. ### Find x where sin(x) gives the same result when expressed in radians or degrees.

The title is pretty much the question, but for more elaboration..: Define the functions...f(x) = sinx where x is measured in radiansg(x) = sinx where x is measured in degrees.On the same set of axes, draw the graphs of both f(x) and g(x) for 0≤x≤20. Indicate on your graph the smallest positive...
6. ### 3tanx + 2cosx = 0 Solving for x but confused

Okay, so, I have been given this question to solve for x and get the possible graph solutions. But I looked at part of the answer and don't understand how some of it works. So the answer is : 3(sinx / cosx) + 2cosx = 0 3sinx + 2cosx / cosx = 0 But then the next line just goes to 3sinx +...
7. ### Thinking Question Help plz

Hi guys, so i need a plan to execute the steps and follow these criterias but i cant even get a head start. Any help would be much appreciated. Thanks guys! Two rational variable expressions are divided and the simplified expression must meet the following conditions: —The simplified...
8. ### Trigonometric functions and three consecutive numbers or non consecutive number

When the triangle is constant (meaning that the base equals to one),the sum of the angles in degrees are 180 Can you mix dimensionless function or angles with lenght in triangles?For example two sides are composed of a distance of $0.85+0.4=1.25$ and at the same time $0.4=\cos\theta$and the...
9. ### Finding theta for all three angles without converting into radian mode

For a triangle of $\angle A B C$ the sides of $a,b,c$ are presented as $a=\frac{\sin A}{\sin C}$, $b=\frac{\sin B}{\sin C}$, $c=\frac{\sin C}{\sin C}$ and the heights $h_a,h_b,h_c$ are written in a form $\frac {h_c}{h_a}=$,$\frac{h_c}{h_b}=$,$\frac{h_c}{h_c}$ to give us $a$ and $b$. and the...
10. ### Trigonometry

Solve 31/2 cos x + sin x =2 1/2 .
11. ### Determine the measure of θ

The question is for the value of sin -√3/2 determine the measure of θ if π/2 ≤ θ ≤ 3π/2. Does it have something to do with special triangles? If so how do I use it solve the problem? The answer is 4π/3 but I don't know how to get there.
12. ### Finding solutions of an equation

Find all of the solutions of the equation cos(56°-3x)=-0.785 where 0° ≤ x ≤ 360° I've been able to find one soloution using x = (56 - arccos(-0.785)) / 3. But I'm unable to find any others. Thanks in advance for any help
13. ### Equating trig identities

Hi, I hope someone can help. It would be great if someone could explain how 2((secx)^4 + 2(secx)^2(tanx)^2) equals -2(cos(2x)-2)(secx)^4 I know that the expressions are related in some way, I just can't pinpoint what. - Olivia
14. ### Function combinations

Hi, I hope someone can help. I'm trying to develop the equation for the following word problem: This is a question from my pre-calculus course, where we are expected to use our knowledge of function combinations to derive an equation for this context. However, I'm finding it to be rather...
15. ### Proving identity

Hi, Does the following expression represent an identity? A student of mine created the expression above and believes that it is an identity. However, I subbed in pi/4 for x on both sides and I got different answers... therefore disproving it as an identity. Can someone please confirm this...
16. ### Finding angle of parallelogram with circle passing through 3 vertices

Given the above construction of parallelogram ABCD, with point E between B and C lying on the circle, the sine of angle A must be greater than √(x)/y where x and y are positive integers. What is the greatest possible value of √(x)/y? Answer: √(5)/3 At first I considered using the law of cosines...
17. ### Flagpole and Building

A 50-ft flagpole stands on the top of a 25-ft building. How far from the base of the building should a person stand if the flagpole and the building are to subtend equal angles at her eye, which is 5 ft above the ground?